Home Page

Branton Campbell in the lab

Branton J. Campbell

Professor

Department of Physics & Astronomy

Brigham Young University

Provo, UT 84602, USA

Tel: 801-422-5758, Fax: 801-422-0553

Email: branton_campbell[at]byu.edu

//physics.byu.edu/faculty/campbell/

Research Interests

I apply state-of-the-art x-ray and neutron scattering techniques to study local and long-range structures in a variety of complex solids, including fast-ion conductors, ferroelectric relaxors, high-temperature superconductors, and colossal magnetoresistive manganites, where nanoscale structural features influence macroscopic physical properties. This includes the development of symmetry-mode analysis as a tool for the determination, refinement and interpretation of distorted structures involving lattice strains, atomic displacements, magnetic moments and occupational orderings at both commensurate and incommensurate wavevectors.

Stellar Diffuse X-ray Scattering

Not astronomy! This is actually single-crystal diffuse x-ray scattering from an important industrial isomerization catalyst called mordenite, where the L = 0 plane of reciprocal space was reconstructed using portions from over 1000 CCD X-ray camera images. The broad patches, open diamonds, and star-shaped distributions are clues that reveal a complex architecture of framework defects with implications for this zeolite’s unusual adsorptive and catalytic properties.

Tabulation of irreducible representations of the crystallographic space groups and their superspace extensions

By Harold T. Stokes, Branton J. Campbell, and Ryan Cordes

Abstract: New tables of irreducible representations (IRs) are introduced for the 230 crystallographic space groups (SGs) in three-dimensional space, at both special and non-special k vectors, and for their extensions to (3 + d)-dimensional superspace ('superspace-extended SGs' or SSESGs). Neither a tabulation of SG IR matrices for non-special k vectors nor a tabulation of SSESG IR matrices for d > 1 have been previously published. These tabulations are made possible by a new form in which the IR matrices of SGs are separated as a product of a translation part T and a point-operation part P, and where the IR matrices of SSESGs are separated as a product of a phase-shift part Q and a point-operation part P-s. Both T and Q have a simple prescribed form that does not need to be tabulated. Also, the new IR matrices are in a convenient block form which allows one to see by inspection which parts of the matrices and the associated order parameters belong to which arm of the star of k. In addition to complex IR matrices, real physically irreducible representation (PIR) matrices are tabulated. The new IR and PIR tables are available on the ISO-IR website (http://stokes.byu.edu/iso/irtables.php) in both convenient human-readable and computer-readable forms.

Phase Progression of γ-Al₂O₃ Nanoparticles Synthesized in a Solvent-Deficient Environment

By Stacey J. Smith, Brian F. Woodfield, Juliana Boerio-Goates, and Branton J. Campbell (et al.)

Abstract:

Our simple and uniquely cost-effective solvent-deficient synthetic method produces 3-5 nm Al2O3 nanoparticles which show promise as improved industrial catalyst supports. While catalytic applications are sensitive to the details of the atomic structure, a diffraction analysis of alumina nanoparticles is challenging because of extreme size/rnicrostrain-related peak broadening and the similarity of the diffraction patterns of various transitional Al2O3 phases. Here, we employ a combination of X-ray pair-distribution function (PDF) and Rietveld methods, together with solid-state NMR and thermogravimetry/differential thermal analysis-mass spectrometry (TG/DTA-MS), to characterize the alumina phase-progression in our nanoparticles as a function of calcination temperature between 300 and 1200 degrees C. In the solvent-deficient synthetic environment, a boehmite precursor phase forms which transitions to gamma-Al2O3 at an extraordinarily low temperature (below 300 degrees C), but this gamma-Al2O3 is initially riddled with boehmite-like stacking-fault defects that steadily disappear during calcination in the range from 300 to 950 degrees C. The healing of these defects accounts for many of the most interesting and widely reported properties of the gamma-phase.

Equivalence of superspace groups

By Branton J. Campbell and Harold T. Stokes (et al.)

Abstract: An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3 + d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3 + d)D. It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two-and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.

Novel Synthesis and Structural Analysis of Ferrihydrite

By Stacey J. Smith, Branton J. Campbell, Juliana Boerio-Goates, and Brian F. Woodfield (et al.)

Abstract: Naturally occurring ferrihydrite is both impure and difficult to isolate, so the numerous applications and interesting properties of ferrihydrite have spurred the development of various synthetic techniques. Nearly all techniques are based on the hydrolysis of an iron salt and require careful control of temperature, pH, and concentration. In this Article, we report a new synthetic method which does not require such control and is perhaps the fastest and simplest route to synthesizing ferrhydrite. XRD, TEM, BET, and chemical purity characterizations show that the chemically pure, 2-line ferrihydrite product consists of crystallites 2-6 nm in diameter which aggregate to form mesoporous, high surface area agglomerates that are attractive candidates for the many adsorption applications of ferrihydrite. X-ray PDF data were also collected for the ferrihydrite product and refined against the hexagonal structural model recently proposed by Michel et al. These analyses suggest that ferrihydrite has a consistent, repeatable structure independent of variation in the synthetic method, water content of the sample, or particle size of the crystallites, and this structure can be adequately described by the proposed hexagonal model.

The superstructure determination of displacive distortions via symmetry-mode analysis

By Sean Kerman, Branton J. Campbell, Kiran K. Satyavarapu, and Harold T. Stokes (et al.)

Abstract: For any crystal structure that can be viewed as a low-symmetry distortion of some higher-symmetry parent structure, one can represent the details of the distorted structure in terms of symmetry-adapted distortion modes of the parent structure rather than the traditional list of atomic xyz coordinates. Because most symmetry modes tend to be inactive, and only a relatively small number of mode amplitudes are dominant in producing the observed distortion, symmetry-mode analysis can greatly simplify the determination of a displacively distorted structure from powder diffraction data. This is an important capability when peak splittings are small, superlattice intensities are weak or systematic absences fail to distinguish between candidate symmetries. Here, the symmetry-mode basis is treated as a binary (on/off) parameter set that spans the space of all possible P1 symmetry distortions within the experimentally determined supercell. Using the average Rwp over repeated local minimizations from random starting points as a cost function for a given mode set, global search strategies are employed to identify the active modes of the distortion. This procedure automatically yields the amplitudes of the active modes and the associated atomic coordinates. The active modes are then used to detect the space-group symmetry of the distorted phase (i.e. the type and location of each of the parent symmetry elements that remain within the distorted supercell). Once a handful of active modes are identified, traditional refinement methods readily yield their amplitudes and the resulting atomic coordinates. A final symmetry-mode refinement is then performed in the correct space-group symmetry to improve the sensitivity to any secondary modes present.